US forces under British command in the Falklands

How would US forces have reacted to serving under British command during the Falklands War?

The forces likely would have worked together effectively, though the political response to that command arrangement is left uncertain.

The discussion expects military cooperation to be easier than agreement over the political commitment. It describes the US Defense Department as often strongly supportive of Britain while the State Department pursued shuttle diplomacy. European positions are also described as changing once Britain's determination to fight became clear. The proposed US deployment under British command remains a counterfactual.